Twisting commutative algebraic groups

If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \otimes_O V$ over $k$, which is a twist of a power of $V$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties.Comment: To appear in Journal of Algebra. Minor changes from original versio

Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates $X$ (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are ``discriminant mixtures of proportional ellipsoidally symmetric'' (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079--1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249--264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.Comment: Published at http://dx.doi.org/10.1214/009053606000000407 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Self-stabilization of extra dimensions

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections, accepted at Phys. Rev.

‘He didn’t even know there was a dictatorship’: the complicity of a psychoanalyst with the Brazilian military regime

The history of psychoanalysis in Brazil during the civilian-military dictatorship (1964-1985) has come under increasing scrutiny in recent years as an instance of institutional complicity with authoritarian rule. The case of Amilcar Lobo in Rio de Janeiro is now well known. However, there is less documentation of events in São Paulo, leading to a misrepresentation of the Brazilian Psychoanalytical Society of São Paulo as having passed relatively unscathed through the dictatorial period. This paper confronts this misrepresentation by documenting the case of a psychoanalyst from São Paulo who was involved with the torture regime. A detailed account is presented of claims made to the authors about the actions of this psychoanalyst in relation to a political prisoner of the period, and some parallels are made with material in two published works by him. It is suggested that this particular psychoanalyst’s behaviour reflects attitudes prevalent in the Brazilian Psychoanalytical Society of São Paulo at the time, including its support for the view that political resistance was a sign of psychological ‘immaturity’ or pathology

Spatial Degrees of Freedom in Everett Quantum Mechanics

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a "core basis problem." To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material tangential to main point remove

Influence of unobservable overstress in a rate-independent inelastic loading curve on dynamic necking of a bar

Proceeding of: IUTAM Symposium on Dynamic Instabilities in Solids, May 17-20, 2016, Madrid, SpainA nonlinear rate-independent overstress model with a smooth elastic-inelastic transition is used to analyze instabilities during dynamic necking of a bar. In the simplified model the elastic strain epsilone determines the value of stress and the hardening parameter kappa determines the onset of inelasticity. These quantities {epsilone, kappa} are obtained by integrating time evolution equations. The main and perhaps surprising result of this paper is that, based on the critical growth rate omegacr of a perturbation, two rate-independent materials with a smooth elastic-plastic transition due to overstress and nearly the same loading curve (elastic strain or stress versus total strain) can have different susceptibilities to tensile instabilities. Specifically, increase in overstress causes decreased material instability near the onset of the smooth elastic-inelastic transition and increased instability when the elastic strain approaches its saturated value. To the authors' knowledge, this new insight has not been reported in the literature.JARM is indebted to the Ministerio de Economía y Competitividad de España (Projects EUIN2015-62556 and DPI2014-57989-P) for the financial support which permitted to conduct part of this work. The research leading to these results has received funding from the European Union’s Horizon2020 Programme (Excellent Science, Marie-Sklodowska-Curie Actions) under REA grant agreement 675602 (Project OUTCOME). This research was also partially supported by MB Rubin’s Gerard Swope Chair in Mechanics

The effect of radial inertia on flow localization in ductile rods subjected to dynamic extension

The objective of this work is to investigate the influence of radial inertia on the flow localization in ductile rods subjected to dynamic extension. Using the theory of a straight Cosserat rod which includes normal cross-sectional extension it is possible to obtain an exact solution for nonlinear uniform extension of a rigid-plastic material using a functional form of the yield stress that models the effect of the more general stress field in the necking region of the rod. Linear stability analysis of this exact nonlinear solution yields equations that generalize the formulation reported in Ref. [1] to include radial stretching and inertia. Examples show the quantitative effect of radial inertia on the stabilization of the localization process and on the determination of the expected length of fragments.This research was partially supported by MB Rubin's Gerard Swope Chair in Mechanics. J. A. Rodríguez-Martínez is indebted to the Ministerio de Ciencia e Innovación de España (Project DPI/2011-24068) for the financial support